Projectile Motion-Definition,Formula,Examples, Concepts,FAQs

What Is Projectile?

A projectile is any object thrown into space upon which the only acting force is gravity. The primary force acting on a projectile is gravity. This doesn’t necessarily mean that other forces do not act on it, just that their effect is minimal compared to gravity. The path followed by a projectile is known as a trajectory. A baseball batted or thrown is an example of a projectile.

What Is Projectile Motion?

When a particle is thrown obliquely near the earth’s surface, it moves along a curved path under constant acceleration directed towards the centre of the earth (we assume that the particle remains close to the earth’s surface). The path of such a particle is called a projectile, and the motion is called projectile motion.

In a Projectile Motion, there are two simultaneous independent rectilinear motions:

1. Along the x-axis: uniform velocity, responsible for the horizontal (forward) motion of the particle.
2. Along the y-axis: uniform acceleration, responsible for the vertical (downwards) motion of the particle.

Acceleration in the horizontal projectile motion and vertical projectile motion of a particle: When a particle is projected in the air with some speed, the only force acting on it during its time in the air is the acceleration due to gravity (g). This acceleration acts vertically downward. There is no acceleration in the horizontal direction, which means that the velocity of the particle in the horizontal direction remains constant.

Parabolic Motion of Projectiles

Let us consider a ball projected at an angle θ with respect to the horizontal x-axis with the initial velocity u as shown below:

The point O is called the point of projection; θ is the angle of projection and OB = Horizontal Range or Simply Range. The total time taken by the particle from reaching O to B is called the time of flight.

For finding different parameters related to projectile motion, we can make use of differential equations of motions:

Total Time of Flight

Resultant displacement (s) = 0 in Vertical direction. Therefore, the time of flight formula is given by using the Equation of motion:

gt² = 2(u_yt – s_y) [Here, u_y = u sin θ and s_y = 0]

i.e. gt² = 2t × u sin θ

Therefore, the time of flight formula (t) is given by:

Total Time of Flight(t)=2usin⁡θ/g

Horizontal Range

Horizontal Range (OA) = Horizontal component of velocity (u_x) × Total Flight Time (t)

R = u cos θ × 2u×sinθ/g

 a projectile motion, the Horizontal Range is given by (R):

Horizontal Range(R)=u²sin⁡2θ/g

Maximum Height of Projectile

After understanding what a projectile is, let us know the maximum height of the projectile. The object’s maximum height is the highest vertical position along its trajectory. The horizontal displacement of the projectile is called the range of the projectile. The range of the projectile depends on the object’s initial velocity.

If u is the initial velocity, g = acceleration due to gravity and H = maximum height in metres, θ = angle of the initial velocity from the horizontal plane (radians or degrees).

The maximum height of the projectile is given by the formula:

H=u²sin2θ/2g

The Equation of Trajectory

EquationofTrajectory=xtan⁡θ − (gx²)/(2u²cos2θ)

This is the equation of trajectory in projectile motion, and it proves that the projectile motion is always parabolic in nature.

Frequently Asked Questions – FAQs

Q1

What is a projectile?

A projectile is any object thrown into space upon which the only acting force is gravity.

Q2

What is a trajectory?

The curved path through which the projectile travels is known as a trajectory.

Q3

Define time of flight.

Time of flight is the measurement of the time taken by an object, particle or wave to travel a distance through a medium.

Q4

Give the time of flight formula?

\(\begin{array}{l}Total\,time\,of\,flight = \frac{2usin\Theta}{g}\end{array} \)

Q5

State true or false: the minimum number of coordinates required to completely define the motion of a body determines the dimension of its motion.

Hope you learned projectile motion, time of flight formula, horizontal range, maximum height, and the equation of trajectory.